Blow-up theorems of Fujita type for a semilinear parabolic equation with a gradient term

Abstract This paper deals with the existence and non-existence of the global solutions to the Cauchy problem of a semilinear parabolic equation with a gradient term. The blow-up theorems of Fujita type are established and the critical Fujita exponent is determined by the behavior of the three variable coefficients at infinity associated to the gradient term and the diffusion–reaction terms, respectively, as well as the spacial dimension